\documentclass[]{article}
\setlength{\pdfpagewidth}{8.5in} \setlength{\pdfpageheight}{11in}

\usepackage{natbib}
           \setlength{\bibhang}{.3in}
           \setlength{\bibsep}{.05in plus0.05in minus0.05in}
           \makeatletter
           \renewcommand{\bibsection}{
           \begin{center}
           \section*{\refname\@mkboth{\MakeUppercase{\refname}}
               {\MakeUppercase{\refname}}}
           \end{center}
           }


	\bibliographystyle{jf}
	
	\begin{document}
	
	 \begin{table}[htbp] 
  \caption{\bf Pricing Ability ($S \& P  \,500$):  local-PCA vs constant-PCA  ($T=24$)}
\medskip
\setlength{\tabcolsep}{3pt}
\begin{tabular}{lccccccccccc}
  \multicolumn{12}{c}{\bf Pricing Ability:  SDF }   \\  \hline 
  \multicolumn{12}{c}{Out-of-Sample}   \\  \hline 
   \# of factors:   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
 \scriptsize{  constant-PCA/local-PCA (bal)} &
    5.318 & 7.899 & 7.639  &  4.673  & 3.535 &  1.578 &  1.245  &  0.891 &  0.663 &  0.569 &  0.445  \\
  \scriptsize{  constant-PCA/local-PCA (unbal)}  &
  9.177 &  36.049 & 129.797 &  7.590 &   2.576 &   1.317 &  0.798 &   0.5244 &   0.403 &   0.302 &   0.221 \\
 \multicolumn{12}{c}{In-Sample}   \\  \hline
 \# of factors:   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
 \scriptsize{  constant-PCA/local-PCA (bal)} &   
   8.148 &  33.674 &   5.518 &   3.271 &   2.181 &   1.584 &   1.215 &   0.932 &   0.743 &   0.615 &   0.501  \\
    \scriptsize{  constant-PCA/local-PCA (unbal)} &  
   0.892 & 33.956 &   2.731 &  1.547 &   1.016 &   0.749 &   0.538 &  0.418 &   0.332 &   0.266 &   0.210 \\
 \multicolumn{12}{c}{\bf Pricing Ability:  Risk Premia }   \\  \hline
 \multicolumn{12}{c}{Out-of-Sample}   \\  \hline
 \# of factors:   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
  \scriptsize{  constant-PCA/local-PCA (bal)} &
  5.694 & 8.098 &  5.604 &  4.190 &  3.279 &  2.644 &  2.175 &  1.816 &  1.531 &  1.299 &  1.108 \\
     \scriptsize{  constant-PCA/local-PCA (unbal)} &
 5.734 &   3.727 &   5.784 &  14.647 &  21.321 &   5.737 &   3.165 &   2.108 &   1.532 &   1.170 &   0.921 \\
    \multicolumn{12}{c}{In-Sample}   \\  \hline
 \# of factors:   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
  \scriptsize{  constant-PCA/local-PCA (bal)}    & 
  7.160 &  34.140  &  6.005 &   4.646 &   5.120 &   4.584 &   3.436 &  3.322 &   2.499 &   1.612 &   1.667 \\
     \scriptsize{  constant-PCA/local-PCA (unbal)} &   
3.028 &   1.994 &   2.596 &   3.060 &   3.523 &   5.474 &  3.432 & 15.286 &  6.1488 & 5.488 &  7.654 \\   \hline  
    \end{tabular}
                   \parbox{7.25in}{\footnotesize{Each entry of this table represents the ratio between the pricing statistics for the constant-PCA over the local-PCA for both the balanced and unbalanced panel case:  ratios (in absolute value)  of  the time-averages (across $636-2T$ windows) of the  bias-adjusted
  SDF pricing statistics $ N^{-1}  \sum_{i=1}^N \tilde{ h}_{i}^2  $  (top two panels)       
        and of the  bias-adjusted
 risk premia pricing statistics  $ N^{-1} \sum_{i=1}^N \tilde{ \delta}_{i}^2  $ described in Theorem~3, 
          (bottom two panels). 
        Panels two and fourth report the in-sample results and panels one and three report the  out-of-sample  results,
    correspondingly to  the (time-varying) estimated number of factors $\tilde{r}$   (column two), described in Section~OA15.1, and to the values one to $ 10 $ (columns 3-12), respectively.  The local-PCA is evaluated with $T=24$. Data are monthly from Dec 1960 until Dec 2013.}}
\label{Table7OASP500}
\end{table}

	
	
\bibliography{Biblio_PCA}


\end{document}
